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Fig. 3. Basic principles and geometric models of optical camera and X-ray
imaging: (a) optical camera and (b) X-ray imaging.

Fig. 2. Video camera and the double mirror construction is physically attached
such, that it has the same optical center and optical axis as the X-ray source.

A. System Components
The C-arm used in the initial setup and in the experiments is
a Siremobile Iso-C 3-D from Siemens Medical Solutions (Erlangen, Germany), a system that is used in our clinical laboratory for both phantom and cadaver studies. The video camera
is the Flea from Point Grey Research, Inc. (Vancouver, BC,
progressive scan
Canada). The camera includes a Sony
CCD, Color with 1024 768 pixel resolution at a frame rate
of 30 FPS. The camera is connected via Firewire connection
(IEEE-1394) to the visualization computer, which is a standard
PC extended by a Falcon framegrabber card from IDS Imaging
Development System GmbH (Obersulm, Germany). The construction to mount the camera and the mirrors are custom made
within our workshop. Without a mirror construction, it is physically impossible to mount the video camera such that the X-ray
source and the camera optical center virtually coincide. The
mirror within the X-ray direction has to be X-ray transparent
in order not to perturb the X-ray image quality. For the experiments presented in this paper, the camera was attached on the
side of the gantry. Another valid and practical option is to attach
the camera on the side of the X-ray source in front of its housing.
Note that the choice between these two options has no effect on
the calibration process or accuracy of the superimposition. We
also developed and adopted an interactive touchpad based user
interface for visualization and guidance (cf. Section II-C).
B. System Calibration
The calibration procedure has to be performed only once
during the initial attachment of the video camera and the double
mirror construction to the gantry of the C-arm. It is valid as
long as the optical camera and the mirror construction are not
moved with respect to the X-ray gantry. The most recent system
setup incorporates the rigidly mounted construction into the
housing of the C-arm gantry. Furthermore, a combined optical
and X-ray marker is introduced to ensure the overlay quality.

This quality assurance has to be performed before every operation. During the pilot studies in the operation room, we have
to assess the quality and validity of the one-time calibration
throughout the lifecycle of the system. The geometric models of
optical and X-ray imaging will be shortly introduced followed
by the calibration routine composed of distortion correction,
physical attachment of the video camera, and estimation of the
1) Model of Optical Cameras: Optical cameras, especially
CCD cameras, are in general modeled as a pinhole camera. The
camera model describes the mapping between 3-D object points
and their corresponding 2-D image points using a central projection. The model in general is represented by an image plane and
a camera center [cf. Fig. 3(a)]. The lens and the CCD sensor are
in general in the same housing. This creates a fixed relationship
between image plane and optical center. The projection geomwith
etry is commonly represented by
projection matrix,
the object point in 3-D and
its corresponding point in the image in projective space [41],
2) Model of X-Ray Imaging: The X-ray imaging is generally
modeled as a point source with rays going through the object
and imaged by the detector plane [cf. Fig. 3(b)]. X-ray geometry is often modeled using the same formulation as the optical
video camera and with the same set of tools of projective geometry. However, in contrast to the optical camera model, the
X-ray source and the detector plane are not rigidly constructed
within one housing. Therefore, the X-ray source and the detector
plane have geometric nonidealities caused by bending of the
C-arm. Compensation for changes in the relative position and
orientation between X-ray source and detector plane can be accomplished using a method based on the definition of a virtual
detector plane [43]. This method consists of imaging markers
located on the X-ray housing near the X-ray source and imaged
on the borders of detector plane. The warping of these points to
fixed virtual positions, often defined by a reference image, guarantees fixed intrinsic parameters, i.e., source-to-detector, image
center, pixel size and aspect ratio. The new 3-D C-arms have
more stable rotational movements and allow us to compute the
required warping to the virtual detector during an offline calibration procedure.
3) Three Step Calibration Procedure: The system calibration
procedure is described and executed in three consecutive steps.
a) Step 1: Distortion Correction: Both the optical video
camera and the X-ray imaging have distortions. The optical
camera distortion is estimated and corrected using standard
computer vision methods. We use a nonlinear radial distortion model and precompute a lookup table for fast distortion